no code implementations • 28 Aug 2022 • Santhosh Karnik, Rongrong Wang, Mark Iwen
The approach is based on the observation that the existence of a Johnson-Lindenstrauss embedding $A\in\mathbb{R}^{d\times D}$ of a given high-dimensional set $S\subset\mathbb{R}^D$ into a low dimensional cube $[-M, M]^d$ implies that for any H\"older (or uniformly) continuous function $f:S\to\mathbb{R}^p$, there exists a H\"older (or uniformly) continuous function $g:[-M, M]^d\to\mathbb{R}^p$ such that $g(Ax)=f(x)$ for all $x\in S$.
no code implementations • 10 Oct 2021 • Michael Perlmutter, Jieqian He, Mark Iwen, Matthew Hirn
We also show that the Gabor measurements used in the second layer can be used to synthesize sparse signals such as those produced by the first layer.
